The Padres have not announced their rotation plans after the Mets series.
Webb is 4-2 with a 3.12 ERA in 40 1/3 innings.
The left-handed hurler left with Miami trailing 3-1. He gave up a sac fly to Chris Young in the second inning before New York took a two-run lead in the fourth inning on an RBI single from opposing pitcher Jacob deGrom and an RBI double from outfielder Curtis Granderson.
Hand was charged with three runs on six hits and two walks, while striking out one. Hand's next start is not yet known since the Marlins have not announced their post-All-Star-break rotation plans.
Hellickson just returned from the disabled list and made his season debut last Tuesday against the Royals. He was sharp, allowing one earned run in 4 1/3 innings.
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"He's starting to do some things at first base and we're segueing probably from DH to first base and eventually to third base," Reds manager Bryan Price said, per MLB.com. "But he's doing some different throws -- like that 3-6-1 double play -- which requires a different arm angle and footwork. So every time we reintegrate something, there's typically a little more soreness afterward, as you would expect while getting into shape.
"So we're taking a step and then we're taking a day off for recovery. He felt great yesterday."